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A. Prove that n3 + 2n is divisible by 3 for all integers n.

A. Prove that n3 + 2n is divisible by 3 for all integers n.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A. Prove that n3 + 2n is divisible by 3 for all integers n. n(3n-1) B. Prove that:1 + 4 +7+..+ (3n – 2) = 2 C. Prove that: п(n+ 1) 2 A. Expand: ( + n) using Pascal's Triangle. B. Expand: (v2x – 3y)" using Binomial Theorem. C. Given the expression: (3x – 2y)15, find the following: a. 5th term b. Middle term c. 10th term d. Last term
Transcribed Image Text:A. Prove that n3 + 2n is divisible by 3 for all integers n. n(3n-1) B. Prove that:1 + 4 +7+..+ (3n – 2) = 2 C. Prove that: п(n+ 1) 2 A. Expand: ( + n) using Pascal's Triangle. B. Expand: (v2x – 3y)" using Binomial Theorem. C. Given the expression: (3x – 2y)15, find the following: a. 5th term b. Middle term c. 10th term d. Last term
1. Prove that 17n³ + 103n is divisible by 6. 2. Write the sigma notation of: 5' 52 + 5° 5"-1 61 - 73 62 – 74 63 - 75T 6" - 7n+2 3. Prove that 13 +23 + 23 + ..+ n3 = n?(n+ 1)2 4. Expand (4x -) using Binomial Theorem 5. Prove that the sum of (") where i is from 0 ton is 2".
Transcribed Image Text:1. Prove that 17n³ + 103n is divisible by 6. 2. Write the sigma notation of: 5' 52 + 5° 5"-1 61 - 73 62 – 74 63 - 75T 6" - 7n+2 3. Prove that 13 +23 + 23 + ..+ n3 = n?(n+ 1)2 4. Expand (4x -) using Binomial Theorem 5. Prove that the sum of (") where i is from 0 ton is 2".
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